Fluid, object, childof constraint animation - won't work
This is a limitation of how blender works, constraints are the last step to placing an object, which means the fluid sim will never see the inflow object in the constrained location.

The way to get this working is to bake the animation into keyframes for the inflow object then remove the constraint. Object->Animation->Bake Action... will do this for you.



You want to turn on visual keying so that you get the location after the constraint is applied.